In offset rotary printing presses, it is highly desirable to prevent penetration of wetting liquid, typically water, in the inking system or inking fountain. One such arrangement to prevent penetration of water is shown in German Utility Model DE-GM 19 04 531. This arrangement provides an additional axially rubbing roller which is beyond the roller train of the inking system, and which is not used for ink transfer. The additional roller is surrounded over part of its circumference by an air blast trough or box or shroud, which provides a stream of drying air in order to dry ink which is transferred to the surface of the additional roller, and which may contain moisture. The publication points out that the diameter of this additional roller must be dimensioned to be of sufficient size so that any wetting liquid which may adhere thereon will be reliably evaporated; the air blast trough of box or shroud which, in part, surrounds this additional roller, should surround a major portion of the circumference of the additional roller. Even if the additional roller is made of substantial size, the surface available to dry ink applied thereto is limited. The quantity of air being supplied thus must be substantial in order to effect the required drying.